This is a very good question in regard to asylees. Read literally, the law says that illegal entry (or entry without inspection, in BCIS lingo) is an inadmissible ground. There is, however, serious doubt as to if Congress really meant to apply this provision to people in asylee status. Various officers are saying different things--some say they will be sticklers while others say they will read the law liberally. Applicants have been asked to submit an EWI waiver. This issue needs to be resolved by senior BCIS mangament at some point, in my view.
However, it appears that they are granting I-602 waivers liberally. If that is indeed the case, then whether this provision applies has no practical effect.